International Association
for Cryptologic Research

Block ciphers such as AES are deterministic, keyed functions that operate on small, fixed-size blocks. Block-cipher \\emph{modes of operation} define a mechanism for probabilistic encryption of arbitrary length messages using any underlying block cipher. A mode of operation can be proven secure (say, against chosen-plaintext attacks) based on the assumption that the underlying block cipher is a pseudorandom function. Such proofs are complex and error-prone, however, and must be done from scratch whenever a new mode of operation is developed.

We propose an \\emph{automated} approach for the security analysis of block-cipher modes of operation based on a ``local\'\' analysis of the steps carried out by the mode when handling a \\emph{single} message block. We model these steps as a directed, acyclic graph, with nodes corresponding to instructions and edges corresponding to intermediate values. We then introduce a set of \\emph{labels} and \\emph{constraints} on the edges, and prove a meta-theorem showing that any mode for which there exists a labeling of the edges satisfying these constraints is secure (against chosen-plaintext attacks). This allows us to reduce security of a given mode to a constraint-satisfaction problem, which in turn can be handled using an SMT solver. We couple our security-analysis tool with a routine that automatically generates viable modes; together, these allow us to synthesize hundreds of secure modes.